TY - JOUR
T1 - Closed ideal planar curves
AU - Andrews, Ben
AU - McCoy, James
AU - Wheeler, Glen
AU - Wheeler, Valentina Mira
N1 - Publisher Copyright:
© 2020, Mathematical Sciences Publishers. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the L2 sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiply covered circle. Moreover, we show that curves in any homotopy class with initially small L3kks k22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.
AB - We use a gradient flow to deform closed planar curves to curves with least variation of geodesic curvature in the L2 sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiply covered circle. Moreover, we show that curves in any homotopy class with initially small L3kks k22 enjoy a uniform length bound under the flow, yielding the convergence result in these cases.
UR - http://www.scopus.com/inward/record.url?scp=85092247476&partnerID=8YFLogxK
U2 - 10.2140/gt.2020.24.1019
DO - 10.2140/gt.2020.24.1019
M3 - Article
SN - 1465-3060
VL - 24
SP - 1019
EP - 1049
JO - Geometry and Topology
JF - Geometry and Topology
IS - 2
ER -